Which of the following numbers is a factor of 126? ${4,7,8,11,12}$
Solution: By definition, a factor of a number will divide evenly into that number. We can start by dividing $126$ by each of our answer choices. $126 \div 4 = 31\text{ R }2$ $126 \div 7 = 18$ $126 \div 8 = 15\text{ R }6$ $126 \div 11 = 11\text{ R }5$ $126 \div 12 = 10\text{ R }6$ The only answer choice that divides into $126$ with no remainder is $7$ $ 18$ $7$ $126$ We can check our answer by looking at the prime factorization of both numbers. Notice that the prime factors of $7$ are contained within the prime factors of $126$ $126 = 2\times3\times3\times7 7 = 7$ Therefore the only factor of $126$ out of our choices is $7$. We can say that $126$ is divisible by $7$.